Your conclusion that it would not be spared sir.
I'm less discussing the strategic facilities and more the "let's not make the whole straits a high-rad zone if we don't need to" idea.
I frankly don't believe such a military base will be left unnuked, seeing other targets...
How long will it be a high-rad zone? and this will hardly affect the Russian fleet. As Condotiere said, it was not powerful in the Mediterranean, and its submarines would not be so affected...